High Energy Physics - Lattice

Abstract: The Banks--Casher relation links the spontaneous breaking of chiral symmetry
in QCD to the presence of a non-zero density of quark modes at the low end of
the spectrum of the Dirac operator. Spectral observables like the number of
modes in a given energy interval are renormalizable and can therefore be
computed using the Wilson formulation of lattice QCD even though the latter
violates chiral symmetry at energies on the order of the inverse lattice
spacing. Using numerical simulations, we find (in two-flavour QCD) that the low
quark modes do condense in the expected way. In particular, the chiral
condensate can be accurately calculated simply by counting the low modes on
large lattices. Other spectral observables can be considered as well and have a
potentially wide range of uses.